We show how the grand unified theory based on the proof of the four
color theorem can be obtained entirely in terms of the Poincare
group of isometries of space and time. Electric and gauge charges
of all the particles of the standard model can now be interpreted
as elements of the Poincare group. We define the space and time
chiralities of all spin 1/2 fermions in agreement with Dirac's
relativistic wave equation. All the particles of the standard model
now correspond to irreducible representations of the Poincare group
according to Wigner's classification. Finally, we construct the
Steiner system of fermions and show how the Mathieu group acts as
the group of symmetries of the fundamental building blocks of
matter.
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